Solution: We can check whether is reducible over Q or not by Eisenstein's criterion.
Let (a prime number). We know that is the coefficient of highest power. Now, we notice that , but since and , i.e., divides all the other coefficients of given polynomial.
We also notice that
Thus, Eisenstein's criterion is satisfied and so, is irreducible over Q[x].
Answer: is irreducible over Q[x].
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